Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory

TL;DR

This paper introduces a novel dispersively improved chiral effective field theory approach to extract the proton charge radius from electron scattering data, avoiding traditional extrapolation issues and achieving results consistent with muonic hydrogen measurements.

Contribution

It combines chiral effective field theory with dispersion analysis to directly determine the proton radius from finite-$Q^2$ data, improving upon previous extrapolation methods.

Findings

Proton radius determined as 0.844(7) fm.

Method effectively constrains radius using finite-$Q^2$ data.

Results align with high-precision muonic hydrogen measurements.

Abstract

We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 = 0$. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to use the finite-$Q^2$ FF data for constraining the radius (up to $Q^2\sim$ 0.5 GeV$^2$ and larger) and avoids the difficulties arising in methods relying on the $Q^2 \rightarrow 0$ extrapolation. We obtain a radius of 0.844(7) fm, consistent with the high-precision muonic hydrogen results.